Classical light microscopy techniques cannot be used directly in imaging most biological structures, as such structures are typically transparent, which is to say that they do not significantly absorb or scatter light, as discussed, for example, by Stevens et al., Light microscopy techniques for live cell imaging, Science, 300, pp. 82-86 (2003), incorporated herein by reference. More particularly, transparency has rendered tomographic imaging of live cells particularly challenging. Therefore this type of imaging has been implemented largely using fluorescence techniques. While confocal fluorescence imaging is a common approach to achieve sectioning, it requires fluorescence probes that are often harmful to a living specimen.
Since it has become increasingly clear that true understanding of cellular function requires high-resolution imaging in three dimensions, various fluorescence techniques have been adapted to work in 3D. Confocal microscopy is the most commonly used technique for 3D imaging and provides an axial resolution of approximately 500 nm. 4Pi microscopy, described by Hell et al., Fundamental Improvement of Resolution with a 4pi-Confocal Fluorescence Microscope using 2-Photon Excitation, Opt. Comm., 93, pp. 277-82 (1992) yields an axial resolution of 90 nm, while, more recently, 3D-STORM (Stochastic Optical Reconstruction Microscopy) provides 50-60 nm resolution. Another approach for 3D re-construction is deconvolution microscopy, in which the blurring of the fluorescence image due to diffraction is treated as a linear problem and reversed numerically. In all of the forgoing methods, only the amplitude (intensity) of the field is measured.
Interference-based methods such as phase-contrast and differential-interference-contrast microscopy, allow imaging such transparent structures without the need for staining or tagging. More advanced methods have introduced the ability to associate quantitative information with a transparent specimen by precisely quantifying optical phase shifts induced by its structure and motion. Spatial light interference microscopy (SLIM), described in US Published Application 2009/0290156 (Popescu et al.), and by Wang et al., Spatial light interference microscopy (SLIM), Opt. Exp., 19, pp. 1016-26 (2011), hereinafter, “Wang (2011a),” both incorporated herein by reference, provide high phase sensitivity imaging of nanoscale structures. SLIM has the important advantage of utilizing illumination characterized by a short-coherence length, and may be implemented via add-on modules added onto existing phase-contrast microscopes.
Depth-sectioning capabilities of SLIM, denominated spatial light interference tomography (SLIT), have been described in Wang et al., Spatial light interference tomography (SLIT), Opt. Exp., 19, pp. 19907-18 (2011), hereinafter, “Wang (2011b),” incorporated herein by reference.
Interference-based microscopy is afflicted by optical degradation and noise, both introduced by the instrument. These degradations can be removed to a certain extent by employing post-processing methods. Deconvolution has been applied as a post-processing method to invert the optical transfer function of the instrument in intensity-based microscopy, as described, for example, by McNally et al., Three-dimensional imaging by deconvolution microscopy, Methods, 19, pp. 373-85 (1999), incorporated herein by reference. Deconvolution works by inverting the optical transfer function of the imaging instrument.
In the case of complex field microscopy, Cotte et al., Microscopy image resolution improvement by deconvolution of complex fields, Opt. Exp., 18, pp. 19462-78 (2010), hereinafter, “Cotte (2010),” which is incorporated herein by reference, investigated the use of complex field deconvolution through inverse filtering in laser-based digital holographic microscopy and reported that the noise amplification, commonly encountered with inverse filtering in intensity-imaging, is not as significant in the case of complex field microscopy. However, due to the laser light illumination, the noise in the images limits the performance of the deconvolution and the overall resolution gain.
A nonlinear deconvolution method developed for SLIM is described in Haldar et al., Label free high-resolution imaging of live cells with deconvolved spatial light interference microscopy, Int. Conf. of the IEEE Eng. in Medicine and Biology Society, pp. 3382-85 (2010), hereinafter, “Haldar (2010)”, which is incorporated herein by reference. Haldar (2010) estimates the unknown magnitude and phase fields via a combination of variable projection and quadratic regularization applied to the phase component. The method of Haldar (2010), however, fails to exploit the sparsity information of biological specimen because the quadratic regularization employed implicitly enforces smoothness on the unknown phase field, even though the phase field is typically not smooth at object boundaries such as fine-scale cell boundaries and intracellular structures. Haldar (2010), moreover, uses a nonlinear conjugate gradient method to obtain both phase and magnitude, which generally contains several approximations and heuristics, and is therefore not as well characterized as linear methods in terms of stability and convergence.
Gazit et al., Super-resolution and reconstruction of sparse sub-wavelength images, Opt. Exp., 17, pp. 23920-46 (2009), hereinafter, “Gazit (2009)”, which is incorporated herein by reference, employed compressed sensing principles to demonstrate resolution increase, in synthetic images, up to five time higher than an artificially imposed resolution limit. The analysis of Gazit (2009) imposes a constraint of exact sparsity in some domain. That is, when represented in a basis, most of the image does not contribute to the measured light energy except only at a few locations. The user is constrained to choosing the support of the non-zero coefficients within this basis, and several thresholds.